Forms of Knowing Mathematics: What Preservice Teachers Should Learn

What important ideas about forms of knowing mathematics should be included in mathematics methods courses for preservice teachers? Ideas are proposed that are related to categories in Shulman's (1986) framework of teacher knowledge. There is a brief discussion of the implications each idea holds for teaching mathematics, and some suggestions are given about experiences that may help preservice teachers appreciate these notions. One portion of Shulman's pedagogical content knowledge construct is knowing what makes a subject difficult and what preconceptions students are apt to bring. Three of the ideas offered for inclusion in a methods course are related to this aspect of pedagogical content knowledge: (1) Understanding students' understanding is important, (2) Students knowing in one way do not necessarily know in the other(s), and (3) intuitive understanding is both an asset and a liability. The last two ideas, are related to the other portion of pedagogical content knowledge, knowing how to make the subject comprehensible to learners. These ideas are (4) certain characteristics of instruction appear to promote retention, and (5) providing alternative representations and recognizing and analyzing alternative methods are important. Readers are asked to consider if the suggestions offered are appropriate and how they might best be taught.     

Why Don't They Understand Us?

The aim of the article is to provide teachers some ideas about thedevelopment of physical knowledge and to make them more receptive to thedifferences between their and the students thinking. I want to show, thatthese differences lie not only in the richness of experience, but also in thestructure of this experience. I try to point to some of these differenceslying in the content, form and meaningfulness. The article is based on anadapted version of Piaget's model of the growth of physical knowledge. Themodel represents the changes of semantic understanding, formal language andlogical structure of a theory during its historical development. I illustratethe model on the development of classical mechanics, but similar changes canbe found also in the history of electrodynamics or quantum mechanics. Thecentral idea of the paper is to use this model of the historical developmentof physical knowledge in analysis of the cognitive processes in physicseducation.     

现代大学应该有什么

现代大学应有先进的教育思想，现代的办学理念；应有一流的人才，一流的成果；应有有利于人才脱颖而出的管理机制，优良的校园文化。     

创新素质教育应遵循的基本原则

创新素质教育必须遵循教育规律，创新素质教育原则是创新素质教育规律的体现。本提出并分析了创新素质教育的探索性原则、活动性原则、开放性原则、超越模仿原则，在此基础上论述了这些原则在教育和教学中的要求。     

Should one develop nonformal education?

In the following pages we are reproducing, with the kind permission of the International Council for Educational Development (ICED) and of Unicef large extracts from a report entitled Nonformal Education for Rural Development: Strengthening Learning Opportunities for Children and Youth' (February 1973).The ICED is a non-profit research organization concerned with improving education's contribution to economic and social development in all the regions of the world.In carrying out this study, at the request of Unicef, Philip H. Coombs was assisted principally by Roy C. Prosser, Deputy Director of the Study; Manzoor Ahmed, Assistant to the Director; Roshan R. Billimoria, Research Assistant, and Sven Grabe, Special Consultant.The main part of the text printed here is drawn from Chapters II and VI of the report. Formerly Director of the International Institute for Educational Planning (Unesco). Currently Vice Chairman of ICED Among his many publications is The World Education Crisis: A Systems Analysis (1968).     

Manipulating Models and Grasping the Ideas They Represent

This article notes the convergence of recent thinking in neuroscience and grounded cognition regarding the way we understand mental representation and recollection: ideas are dynamic and multi-modal, actively created at the point of recall. Also, neurophysiologically, re-entrant signalling among cortical circuits allows non-conscious processing to support our deliberative thoughts and actions. The qualitative research we describe examines the exchanges occurring during semi-structured interviews with 360 children age 3–13, including 294 from New Zealand (158 boys, 136 girls) and 66 from China (34 boys, 32 girls) concerning their understanding of the shape and motion of the Earth, Sun and Moon (ESM). We look closely at the relationships between what is revealed as children manipulate their own play-dough models and their apparent understandings of ESM concepts. In particular, we focus on the switching taking place between what is said, what is drawn and what is modelled. The evidence is supportive of Edelman’s view that memory is non-representational and that concepts are the outcome of perceptual mappings, a view which is also in accord with Barsalou’s notion that concepts are simulators or skills which operate consistently across several modalities. Quantitative data indicate that the dynamic structure of memory/concept creation is similar in both genders and common to the cultures/ethnicities compared (New Zealand European and Māori; Chinese Han) and that repeated interviews in this longitudinal research lead to more advanced modelling skills and/or more advanced shape and motion concepts, the results supporting hypotheses (Kolmogorov–Smirnov alpha levels .05; r _s : p < .001).     

They do care: An interview with William Damon and Anne Colby on moral development

What follows is an interview with William Damon and Anne Colby, pioneers in the fields of moral psychology and education. Throughout their careers, they have studied, moral identity, moral ideals, positive youth development, purpose, good work, vocation, character development in higher education, and professional responsibility. In their words, they are interested in the ‘best of humankind’—not only the competencies, but also the character necessary for living a good life—not only for the sake of the individual, but also for society. They have received numerous academic and civic awards and honors. Their publications include Some Do Care, Greater Expectations, Educating Citizens, The Path to Purpose, and most recently, The Power of Ideals—in addition to editing, for example, New Directions for Child and Adolescent Development and The Handbook of Child Psychology. As a married couple, their vocational journeys have mostly been separate, but have always complemented each other and sometimes converged. This interview asks about reflections on their careers, their own sense of purpose, their greatest contributions, current needs in our field, and advice to emerging scholars.     

Developing knowledge intensive ideas in engineering education: the application of camp methodology

Background: Globalization, technological advancement, environmental problems, etc. challenge organizations not just to consider cost-effectiveness, but also to develop new ideas in order to build competitive advantages. Hence, methods to deliberately enhance creativity and facilitate its processes of development must also play a central role in engineering education. However, so far the engineering education literature provides little attention to the important discussion of how to develop knowledge intensive ideas based on creativity methods and concepts.

Purpose: The purpose of this article is to investigate how to design creative camps from which knowledge intensive ideas can unfold.

Design/method/sample: A framework on integration of creativity and knowledge intensity is first developed, and then tested through the planning, execution and evaluation of a specialized creativity camp with focus on supply chain management. Detailed documentation of the learning processes of the participating 49 engineering and business students is developed through repeated interviews during the process as well as a survey.

Results: The research illustrates the process of development of ideas, and how the participants through interdisciplinary collaboration, cognitive flexibility and joint ownership develop highly innovative and knowledge-intensive ideas, with direct relevance for the four companies whose problems they address.

Conclusions: The article demonstrates how the creativity camp methodology holds the potential of combining advanced academic knowledge and creativity, to produce knowledge intensive ideas, when the design is based on ideas of experiential learning as well as creativity principles. This makes the method a highly relevant learning approach for engineering students in the search for skills to both develop and implement innovative ideas.     

Should Eudaimonia Structure Professional Virtue?

This article develops a eudaimonistic account of professional virtue. Using the case of teaching, the article argues that professional virtue requires that role holders care about the ends of their work. Care is understood in terms of an investment of the self. Virtuous role holders are invested in their practice in a way that makes professional excellence part of their own good. Failure to care about the ends of professional practice reveals a lack of appreciation of the value of professional work. This ‘investment view’ is contrasted with the currently popular ‘key goods view’, which claims that professional virtues require a profession‐specific teleological structure. Unlike ordinary virtues, which are governed by eudaimonia or human flourishing, professional virtues are allegedly derived from professional ends, like health or education. The article argues that this delivers an unconvincing criterion for determining the merits of character traits.     

Welcoming Opposition: Havruta Learning and Montaigne’s The Art of Discussion

Michel de Montaigne’s L’art de Conférer offers a moral groundwork for students’ learning of havruta, a traditional Jewish form of studying in pairs, based on collaborative critical text-based learning, that can be applied to students everywhere. The article attends to the nature of havruta learning and to cultural norms that make it difficult for students to become open to their partners’ opposing ideas. Students’ critical discussion of Montaigne’s essay is then conceptualized as a pedagogical tool for cultivating the welcoming of opposing viewpoints and opening their own ideas to critical scrutiny in text- and discussion-based learning. I draw on Wolfgang Iser’s theory of reading as bringing the reader into deeper self-consciousness and calling into question implicit beliefs about the role of opposing ideas. The article provides an analysis of Montaigne’s ideas and includes study questions to help students adopt a more constructive attitude toward opposing views and expand their understanding of the role of the confrontation of ideas in learning discussions.     

高校图书馆要面向社会服务

文章论述了高校图书馆面向社会服务的重要性和必要性以及如何开展面向社会用户服务的思路。     

个性化教学:教师的难为与应为

21世纪的社会呼唤富有个性和创造性的人才,教育应该重视以全面发展学生个性为目的的个性化教学。教师在个性化教学要求下,存在"应为却难为"的状况。基于此,从教学理念的形成、教学目标的定位、教学过程的实施和教师的自我发展四个方面分析教师在个性化教学要求下的"难为"与"应为"。     

高校图书馆应主动为学生服务

高校图书馆应打破传统观念 ,主动架起学生和知识的桥梁 ,为学生提供更好的现代化的优质服务     

Interaction of the originality of peers’ ideas and students’ openness to experience in predicting creativity in online collaborative groups

There has been growing interest in the possibility that peers’ ideas can stimulate students’ creativity in group contexts. However, empirical research on this issue is limited. This study tested the hypothesis that peers’ ideas and students’ openness to experience would predict student creativity and attention to peers’ ideas. Undergraduate students (n = 60) completed creative tasks in an online collaborative group in which the ideas of “peers” were pre-programmed. Mixed ANOVAs showed support for the hypothesis. Specifically, students with higher (but not lower) openness, when exposed to a high (but not low) rate of peers’ original ideas, paid greater attention to those ideas and were more creative. The implication for education is that teachers should encourage students to share more of their original ideas and to pay more attention to peers’ ideas in online collaborative groups.     

A Balancing Act: Developing a Discourse Community in a Mathematics Classroom

This article examines the pedagogical tensions involved in trying to usestudents' ideas as the basis for class discussion while also ensuring thatdiscussion is productive mathematically. The data for this study of theteaching of one middle-school teacher come from observations andvideotapes of instruction across a school year as well as interviews with theparticipating teacher. Specifically, the article describes the teacher'sattempts to support a student-centered process of mathematicaldiscourse and, at the same time, facilitate discussions of significantmathematical content. This tension in teaching was not easily resolved;throughout the school year the teacher shifted his emphasis betweenmaintaining the process and the content of the classroom discourse.Nevertheless, at times, the teacher balanced these competing goals by usinga ``filtering approach' to classroom discourse. First multiple ideas aresolicited from students to facilitate the process of student-centeredmathematical discourse. Students are encouraged to elaborate theirthinking, and to compare and evaluate their ideas with those that havealready been suggested. Then, to bring the content to the fore, the teacherfilters the ideas, focusing students' attention on a subset of themathematical ideas that have been raised. Finally, the teacher encouragesstudent-centered discourse about these ideas, thus maintaining a balancebetween process and content.     

应把中等职业教育纳入教育督导评估体系

本文阐述了在大力发展职业教育的新形势下．把职业教育纳入教育督导评估体系的必要性，同时也对实施职业教育督导评估提出了几点建议和设想。     

Learning from Chemical Visualizations: Comparing generation and selection

Dynamic visualizations can make unseen phenomena such as chemical reactions visible but students need guidance to benefit from them. This study explores the value of generating drawings versus selecting among alternatives to guide students to learn chemical reactions from a dynamic visualization of hydrogen combustion as part of an online inquiry unit. In prior research, generation has been more successful than selection in helping students distinguish among ideas to learn complex topics. However, selecting among perplexing alternatives may motivate learners to distinguish among ideas they might otherwise neglect. To test the value of selection for helping students distinguish ideas, this study contrasted complex selection (involving normative as well as non-normative ideas identified in prior research) from typical selection (involving images from the visualization). Results showed that all conditions improved student understanding and that typical selection was less effective than generation while complex selection was as successful as generation. In both generation and complex selection students revisited the visualization while learning, whereas revisiting was rare in typical selection. These results support the idea that distinguishing among common non-normative ideas is more valuable than distinguishing among images from the visualization. In addition, for students with low prior knowledge, both generation and complex selection had some advantages. Overall, the results suggest that students learning from complex visualizations could benefit from a combination of complex selection and generation.     

Problematising the theory–practice terminology: a discourse analysis of students’ statements on Work-integrated Learning

ABSTRACT

This study uses a Foucault-inspired discourse analysis to examine two ideas about learning which reinforce the terminology whereby theory means campus-based training and practice means work placements. The purpose is to problematise this theory–practice terminology and provide scope for a non-dualistic alternative. The ideas examined are the idea of theory vs. practice as the point of departure for learning and the idea of theory and practice as harmonious points of departure for learning. These ideas were voiced by interviewed students who discussed the usual design of Work-integrated Learning (WIL) whereby students go to university to learn ‘theory’ and into working life to learn ‘practice’. The analysis shows how the ideas are formed by different ranking orders between theory and practice which are mutually exclusive, while also working together to reinforce the theory–practice terminology. The discussion on how a non-dualistic terminology can emerge highlights how the usual WIL design forms a dualistic setting where the theory–practice terminology thrives and how designing WIL at a third place between university and working life can provide scope for the terminology we seek.     

Fostering thinking through science in the early years of schooling

The purpose of this research was to investigate and describe concrete examples of Year 1 students engaged in good thinking and to generate assertions about the ways teachers can foster habits of good thinking through science. The research design was a multiple case study of 32 lessons, of which four are analysed in detail in this paper. The results suggest that young children engaged in good thinking are likely to explain and demonstrate their ideas and actions and to make suggestions for solving problems. Children engaged in good thinking also are likely to highlight discrepancies, adopt new ideas, and work collaboratively. The results indicate that teachers can foster habits of good thinking through science; first, by accepting difficulty as an integral part of the learning process, second, by encouraging children to explain and talk about their ideas and, finally, by creating an environment where thinking is a valued classroom process.